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• Chapter 7 Multidimensional Arrays Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 1
• MotivationsThus far, you have used one-dimensional arrays to model linearcollections of elements. You can use a two-dimensional array torepresent a matrix or a table. For example, the following table thatdescribes the distances between the cities can be represented using atwo-dimensional array. Distance Table (in miles) Chicago Boston New York Atlanta Miami Dallas Houston Chicago 0 983 787 714 1375 967 1087 Boston 983 0 214 1102 1763 1723 1842 New York 787 214 0 888 1549 1548 1627 Atlanta 714 1102 888 0 661 781 810 Miami 1375 1763 1549 661 0 1426 1187 Dallas 967 1723 1548 781 1426 0 239 Houston 1087 1842 1627 810 1187 239 0 1723 1548 781 1426 0 239 Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 2
• Objectives To give examples of representing data using two-dimensional arrays (§7.1). To declare variables for two-dimensional arrays, create arrays, and access array elements in a two-dimensional array using row and column indexes (§7.2). To program common operations for two-dimensional arrays (displaying arrays, summing all elements, finding min and max elements, and random shuffling) (§7.3). To pass two-dimensional arrays to methods (§7.4). To write a program for grading multiple-choice questions using two- dimensional arrays (§7.5). To solve the closest-pair problem using two-dimensional arrays (§7.6). To check a Sudoku solution using two-dimensional arrays (§7.7). To use multidimensional arrays (§7.8). Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 3
• Declare/Create Two-dimensional Arrays// Declare array ref vardataType[][] refVar;// Create array and assign its reference to variablerefVar = new dataType[10][10];// Combine declaration and creation in one statementdataType[][] refVar = new dataType[10][10];// Alternative syntaxdataType refVar[][] = new dataType[10][10]; Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 4
• Declaring Variables of Two- dimensional Arrays and Creating Two-dimensional Arraysint[][] matrix = new int[10][10];orint matrix[][] = new int[10][10];matrix[0][0] = 3;for (int i = 0; i < matrix.length; i++) for (int j = 0; j < matrix[i].length; j++) matrix[i][j] = (int)(Math.random() * 1000);double[][] x; Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 5
• Two-dimensional Array Illustration [0] [1] [2] [3] [4] [0] [1] [2] [3] [4] [0] [1] [2] [3] 4[0] 0 0 0 0 0 [0] 4 0 0 0 0 0 [0] 1 2 3[1] 0 0 0 0 0 [1] 0 0 0 0 0 [1] 4 5 6[2] 0 0 0 0 0 [2] 0 7 0 0 0 [2] 7 8 9[3] 0 0 0 0 0 [3] 0 0 0 0 0 [3] 10 11 12[4] 0 0 0 0 0 [4] 0 0 0 0 0 [4] int[][] array = { {1, 2, 3},matrix = new int[5][5]; matrix[2][1] = 7; {4, 5, 6}, {7, 8, 9}, {10, 11, 12} }; matrix.length? 5 array.length? 4 matrix[0].length? 5 array[0].length? 3 Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 6
• Declaring, Creating, and Initializing Using Shorthand NotationsYou can also use an array initializer to declare, create and initialize a two-dimensional array. For example,int[][] array = { int[][] array = new int[4][3]; {1, 2, 3}, array[0][0] = 1; array[0][1] = 2; array[0][2] = 3; {4, 5, 6}, Same as array[1][0] = 4; array[1][1] = 5; array[1][2] = 6; {7, 8, 9}, array[2][0] = 7; array[2][1] = 8; array[2][2] = 9; {10, 11, 12} array[3][0] = 10; array[3][1] = 11; array[3][2] = 12;}; Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 7
• Lengths of Two-dimensional Arrays int[][] x = new int[3][4];x x[0][0] x[0][1] x[0][2] x[0][3] x[0].length is 4 x[0] x[1] x[1][0] x[1][1] x[1][2] x[1][3] x[1].length is 4 x[2] x[2][0] x[2][1] x[2][2] x[2][3] x[2].length is 4x.length is 3 Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 8
• Lengths of Two-dimensional Arrays, cont.int[][] array = { array.length {1, 2, 3}, array[0].length {4, 5, 6}, array[1].length {7, 8, 9}, array[2].length {10, 11, 12} array[3].length}; array[4].length ArrayIndexOutOfBoundsException Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 9
• Ragged ArraysEach row in a two-dimensional array is itself an array. So, the rows can have different lengths. Such an array is known as a ragged array. For example,int[][] matrix = { {1, 2, 3, 4, 5}, matrix.length is 5 {2, 3, 4, 5}, matrix[0].length is 5 matrix[1].length is 4 {3, 4, 5}, matrix[2].length is 3 {4, 5}, matrix[3].length is 2 {5} matrix[4].length is 1}; Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 10
• Ragged Arrays, cont.int[][] triangleArray = { 1 2 3 4 5 {1, 2, 3, 4, 5}, {2, 3, 4, 5}, 2 3 4 5 {3, 4, 5}, {4, 5}, 3 4 5 {5}}; 4 5 5 Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 11
• Processing Two-Dimensional ArraysSee the examples in the text.1. (Initializing arrays with input values)2. (Printing arrays)3. (Summing all elements)4. (Summing all elements by column)5. (Which row has the largest sum)6. (Finding the smallest index of the largest element)7. (Random shuffling) Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 12
• Initializing arrays with input valuesjava.util.Scanner input = new Scanner(System.in);System.out.println("Enter " + matrix.length + " rows and " + matrix[0].length + " columns: ");for (int row = 0; row < matrix.length; row++) { for (int column = 0; column < matrix[row].length; column++) { matrix[row][column] = input.nextInt(); }} Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 13
• Initializing arrays with random valuesfor (int row = 0; row < matrix.length; row++) { for (int column = 0; column < matrix[row].length; column++) { matrix[row][column] = (int)(Math.random() * 100); }} Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 14
• Printing arraysfor (int row = 0; row < matrix.length; row++) { for (int column = 0; column < matrix[row].length; column++) { System.out.print(matrix[row][column] + " "); } System.out.println();} Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 15
• Summing all elementsint total = 0;for (int row = 0; row < matrix.length; row++) { for (int column = 0; column < matrix[row].length; column++) { total += matrix[row][column]; }} Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 16
• Summing elements by columnfor (int column = 0; column < matrix[0].length; column++) { int total = 0; for (int row = 0; row < matrix.length; row++) total += matrix[row][column]; System.out.println("Sum for column " + column + " is " + total);} Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 17
• Random shufflingfor (int i = 0; i < matrix.length; i++) { for (int j = 0; j < matrix[i].length; j++) { int i1 = (int)(Math.random() * matrix.length); int j1 = (int)(Math.random() * matrix[i].length); // Swap matrix[i][j] with matrix[i1][j1] int temp = matrix[i][j]; matrix[i][j] = matrix[i1][j1]; matrix[i1][j1] = temp; }} Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 18
• Passing Tow-Dimensional Arrays to Methods PassTwoDimensionalArray Run Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 19
• Problem: Grading Multiple- Choice Test  Objective: write a Students’ Answers to the Questions: 0 1 2 3 4 5 6 7 8 9 program that gradesStudent 0 A B A C C D E E A D multiple-choice test.Student 1 D B A B C A E E A DStudent 2 E D D A C B E E A DStudent 3 C B A E D C E E A D Key to the Questions:Student 4 A B D C C D E E A D 0 1 2 3 4 5 6 7 8 9Student 5 B B E C C D E E A DStudent 6 B B A C C D E E A D Key D B D C C D A E A DStudent 7 E B E C C D E E A D GradeExam Run Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 20
• Problem: Finding Two Points Nearest to Each Other x y 0 -1 3 (-1, 3) (3, 3) 1 -1 -1 2 1 1 (4, 2) (1, 1) 3 2 0.5 4 2 -1 (2, 0.5) 5 3 3 (4, -0.5) 6 4 2(-1, -1) (2, -1) 7 4 -0.5 FindNearestPoints Run Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 21
• What is Sudoku?5 3 76 1 9 5 9 8 68 6 34 8 3 17 2 6 6 4 1 9 5 8 7 9 Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 22
• Every row contains the numbers 1 to 95 3 7 5 3 4 6 7 8 9 1 26 1 9 5 6 7 2 1 9 5 3 4 8 9 8 6 1 9 8 3 4 2 5 6 78 6 3 8 5 9 7 6 1 4 2 34 8 3 1 4 2 6 8 5 3 7 9 17 2 6 7 1 3 9 2 4 8 5 6 6 9 6 1 5 3 7 2 8 4 4 1 9 5 2 8 7 4 1 9 6 3 5 8 7 9 3 4 5 2 8 6 1 7 9 Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 23
• Every column contains the numbers 1 to 95 3 7 5 3 4 6 7 8 9 1 26 1 9 5 6 7 2 1 9 5 3 4 8 9 8 6 1 9 8 3 4 2 5 6 78 6 3 8 5 9 7 6 1 4 2 34 8 3 1 4 2 6 8 5 3 7 9 17 2 6 7 1 3 9 2 4 8 5 6 6 9 6 1 5 3 7 2 8 4 4 1 9 5 2 8 7 4 1 9 6 3 5 8 7 9 3 4 5 2 8 6 1 7 9 Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 24
• Every 3×3 box contains the numbers 1 to 95 3 7 5 3 4 6 7 8 9 1 26 1 9 5 6 7 2 1 9 5 3 4 8 9 8 6 1 9 8 3 4 2 5 6 78 6 3 8 5 9 7 6 1 4 2 34 8 3 1 4 2 6 8 5 3 7 9 17 2 6 7 1 3 9 2 4 8 5 6 6 9 6 1 5 3 7 2 8 4 4 1 9 5 2 8 7 4 1 9 6 3 5 8 7 9 3 4 5 2 8 6 1 7 9 Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 25
• Checking Whether a Solution Is Correct 5 3 7 5 3 4 6 7 8 9 1 2 6 1 9 5 6 7 2 1 9 5 3 4 8 9 8 6 1 9 8 3 4 2 5 6 7 8 6 3 8 5 9 7 6 1 4 2 3 4 8 3 1 4 2 6 8 5 3 7 9 1 7 2 6 7 1 3 9 2 4 8 5 6 6 9 6 1 5 3 7 2 8 4 4 1 9 5 2 8 7 4 1 9 6 3 5 8 7 9 3 4 5 2 8 6 1 7 9 CheckSudokuSolution Run Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 26
• Multidimensional ArraysOccasionally, you will need to represent n-dimensional data structures. In Java, you can createn-dimensional arrays for any integer n.The way to declare two-dimensional arrayvariables and create two-dimensional arrays can begeneralized to declare n-dimensional arrayvariables and create n-dimensional arrays for n >=3. Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 27
• Multidimensional Arrays double[][][] scores = { {{7.5, 20.5}, {9.0, 22.5}, {15, 33.5}, {13, 21.5}, {15, 2.5}}, {{4.5, 21.5}, {9.0, 22.5}, {15, 34.5}, {12, 20.5}, {14, 9.5}}, {{6.5, 30.5}, {9.4, 10.5}, {11, 33.5}, {11, 23.5}, {10, 2.5}}, {{6.5, 23.5}, {9.4, 32.5}, {13, 34.5}, {11, 20.5}, {16, 7.5}}, {{8.5, 26.5}, {9.4, 52.5}, {13, 36.5}, {13, 24.5}, {16, 2.5}}, {{9.5, 20.5}, {9.4, 42.5}, {13, 31.5}, {12, 20.5}, {16, 6.5}}};Which student Which exam Multiple-choice or essay scores[ i ] [ j ] [ k ] Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 28
• Problem: Calculating Total Scores Objective: write a program that calculates the total score for students in a class. Suppose the scores are stored in a three- dimensional array named scores. The first index in scores refers to a student, the second refers to an exam, and the third refers to the part of the exam. Suppose there are 7 students, 5 exams, and each exam has two parts--the multiple-choice part and the programming part. So, scores[i][j][0] represents the score on the multiple-choice part for the i’s student on the j’s exam. Your program displays the total score for each student. TotalScore Run Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 29
• Problem: Weather Information Suppose a meteorology station records the temperature and humidity at each hour of every day and stores the data for the past ten days in a text file named weather.txt. Each line of the file consists of four numbers that indicate the day, hour, temperature, and humidity. Your task is to write a program that calculates the average daily temperature and humidity for the 10 days.1 1 76.4 0.92 10 24 98.7 0.741 2 77.7 0.93 1 2 77.7 0.93... ...10 23 97.7 0.71 10 23 97.7 0.71 Weather10 24 98.7 0.74 1 1 76.4 0.92 (b) (a) Run Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 30
• Problem: Guessing Birthday Listing3.8, GuessBirthday.java, gives a program that guesses a birthday. The program can be simplified by storing the numbers in five sets in a three-dimensional array, and it prompts the user for the answers using a loop, as shown in Listing 7.6. The sample run of the program can be the same as shown in Listing 3.8. GuessBirthdayUsingArray Run Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All rights reserved. 31